Finite Group Databasebeta

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C2×C5×C17×C49⋊C3 #38735912

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C17×C49⋊C3
unambiguous semidirect product(C2×C49)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C5×C49)⋊(C3×C17)
unambiguous semidirect product(C2×C17×C49)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C17×C49)⋊C3

Splittings

Fitting, HallC2×C5×C17×C49 ⋊ C3
derived, SylowC49 ⋊ C2×C3×C5×C17
HallC5×C17×C49 ⋊ C2×C3
HallC2×C17×C49 ⋊ C3×C5
HallC17×C49 ⋊ C2×C3×C5
HallC2×C5×C49 ⋊ C3×C17
HallC5×C49 ⋊ C2×C3×C17
HallC2×C49 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17C49⋊C3
commutator, cosocle, hypocenterC49C2×C3×C5×C17
FrattiniC7C2×C5×C17×ΓL(1,𝔽8)
FittingC2×C5×C17×C49C3
socleC2×C5×C7×C17ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C2×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8330

Conjugacy classes & character table

3230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 2);